Question

A convex lens ‘A’ of focal length 20 cm and a concave lens ‘B’ of focal length 5 cm are kept along the same axis with a distance ‘d’ between them. If a parallel beam of light falling on ‘A’ leaves ‘B’ as a parallel beam, then the distance ‘d’ in cm will be

• A. 30
• B. 25
• C. 15
• D. 50

Answer 1

The Correct Option is C

To solve this problem, we need to understand the concept of lenses and their combination. Specifically, we're dealing with a convex lens and a concave lens placed on the same optical axis, and we want a parallel beam of light entering the convex lens to exit the concave lens also as a parallel beam.

Let's break down the problem into step-by-step logical explanations and calculations:

Given:

• The focal length of the convex lens 'A' (\( f_A \)) is 20 cm.
• The focal length of the concave lens 'B' (\( f_B \)) is -5 cm (note: concave lenses have negative focal lengths).

When a parallel beam of light is incident on the convex lens, it will converge to its focal point, which is 20 cm away from lens 'A'.

For the light to leave lens 'B' as a parallel beam, the light should emerge from the focal point of lens 'B', which is 5 cm away from it on the side where the beam would converge.

The objective is to make these conditions meet; that is, the image formed by the convex lens should serve as the object for the concave lens at its focal point.

This implies the distance 'd' between the two lenses should be such that the object (virtual in this case, as it comes from lens 'A') is positioned at the focal point of lens 'B'. Therefore, the combined setup is:

\(d = f_A - f_B = 20 \, \text{cm} - (-5 \, \text{cm}) = 20 \, \text{cm} + 5 \, \text{cm} = 15 \, \text{cm}\)

Thus, the required distance \(d\) is 15 cm, which makes option 15 the correct answer.